' = 
t 
boatoatt 
| ies 
# i<} 
ae as bs Saaz aeunasves za Ss Ei }! 
tp 
; 
eh . 
if 
a L 
he 2 bad 
S| ares 
TS 
y 
1 
ei 
z Beier: nee . — 


THE UNIVERSITY 
OF ILLINOIS 
LIBRARY 


MATHEMATICS LIBRARY 


The person charging this material is re- 
sponsible for its return to the library from 
which it was withdrawn on or before the 
Latest Date stamped below. 

Theft, mutilation, and underlining of books are reasons 
for disciplinary action and may result in dismissal from 


the University. 
To renew call Telephone Center, 333-8400 


| 
| 


UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN 


PALMER’S 


t 


POCKET SCALE, 


FOR ITS USE IN SOLVING 


ARITHMETICAL AND GEOMETRICAL 


’ 
PROBLEMS. od 
HHE LIBRARY OF THe 


a" - 
ve ROCHESTER: te 
PUBLISHED BY AARON PALMER. 

Canfield & Warren, Printers. tee? 
1845. 


“G 


mS 


RS eo ee wrens, 


core OF 
a fi \ y 
% | if MATE NM +t ‘pes IBRARY 
PALMER’S 


ENDLESS SELF-COMPUTING SCALE. 


Tue proprietors of this invaluable work, beg leave to pre- 
sent the public with the following notice: 

This Scale (the result of three years’ incessant labor) is 
designed as an assistant in, all arithmetical calculations. 


The simplicity, rapidity, and accuracy of its results have — 


astonished our best mathematicians. It consists of a log- 
arithmic combination of numbers, arranged in two or more 
circles, one of which is made to revolve within the other; 
which process constantly changes the relation of the figures 
to each other, and solves an infinite variety of problems. 
Its advantages are— 


Ist. A complete saving of mental labor ; for, by the use of 
this Scale, the most intricate calculations are but a 
pleasurable exercise of the mind. 


Qd. A great saving of time. Computations requiring from 
three to four days, are wrought out by this Scale in 
the incredible short space of one minute. 


3d. Complete accuracy. The results of the computations 
on this Scale are infallible. Errors are entirely out 
of the question, except through sheer carelessness. 


4th. Mental improvement. By this Scale, a knowledge of 
the philosophy of numbers, and their relation to each 
other, is soon obtained. So that, in a little time, 
many of the common calculations are wrought out 
by the mere exercise of the mind e 
ies, 
ae 


791940 « 


RECOMMENDATIONS 


OF THE 


ENDLESS SELF-COMPUTING SCALE. 


Rocuester, Jan. 19, 1842. 
Tue “Self-Computing Scale,” by A. Palmer, is'a very 
ingenious and interesting instrument. for performing most 
of the operations in arithmetic. The principle is very plain ; 
and the accuracy, and certainty, and rapidity of the results 
are very striking. Cc. DEWEY, 
PRindipal of Collegiate Institute. 


Rocusster, Jan. 19, 1842. 
Having particularly examined Mr. Palmer’s “ Self-Com- 
_ puting Scale,” I fully concur in the above testimonials of 
Dr. Dewey. SAMUEL LUCKEY, D. D. 


——o 


Arrica, Marcu 5, 1842. 
From an examination of the ‘Self-Computing Scale,” 
by Mr. Palmer, I can most cheerfully concur in the above 
recommendations, and hope it may be introduced into our 
schools and academies. 
E. B. WALSWORTH, 
Principal of Attica Academy 


Burra.to, Apriz 5, 1842. 
We have examined the above-mentioned Scale, and con 
cur i n the certificate of Professor Dewey. 
W. K. SCOTT, Civ. Eng. 
R. W. HASKIN S, M. A. 


ae 

fi Brockrort, Fs. 19, 1842. 
I have carefully examined “The Endless Self-Comp 
ting Scale,” by Mr. Aaron Palmer; and without hesitation 
: give it.as my opinion, that it will be found a very useful in- 


* 


inte iy 


& 5 


vention. All the problems in arithmetic can be read_ly 
solved upon it, and most of them with great expedition, 
particularly the rules for computing interest for months and 
days, at any per cent., the rule of three, and fractions. In 
the apportionment of county, town, and school taxes, it will 
be found almost invaluable, as it requires to be set but once, 
to show each man’s tax. 
JULIUS BATES, M. A., 
Principal of Collegiate Institute. 


CamsripcE, Ocr. 20, 1843. 

I have examined Mr. Aaron Palmer’s ‘ Endless Self- 

Computing Scale 3 it is simple and most ingenious, and I 

cheerfully concur in Mr. Julius Bates’s judicious recommen- 
dations of its utility. 

BENJAMIN PEIRCE, 

Perkins Professor of Astronomy and Mathematics 
in Harvard University. 


Boston, Ocr. 24, 1843. 
Mr. Palmer’s “ Self-Computing Scale” is certainly a very 
ingenious arrangement.of numbers, and it will save a great 
amount of time in the hands of those who have computing 
to perform, whatever be the subject of the computation. 
FREDERICK EMERSON, 
Author of the North American Ar ithmetic. 


I heartily concur in the above recommendation. 
WM. B. FOWLE, 
Late Teacher of the Female Monitorial School, Boston. 


Besron, Oct. 23, 1843. 
Mr. Aaron PaLmMER— 

Sir: Your “Self-Computing Scale” appear to me an 
exceedingly useful invention. I shall be glad to possess one 
of them, as it will save me much labor; and I doubt not 
that many persons will find the same advantage in its use. 

Respectfully your servant, 
JOHN 8. TYLER, 
sie ‘Shey: and Insurance Broker. 


« 


i, 


6 * 


Boston, Oct. 24, 1843. 

I bate examined Mr. Aaron Palmer’s “ Self-Computing 
Scale ;” it strikes me as being a very convenient labor- 
saving machine, and that it will be highly useful in caleu- 
lating interest, general average, or dividends on a bank- 
rupt’s estate, and for other similar purposes. 

S. E. SEWELL, Counsellor at Law. 


I have examined “ The Endless Self-Computing Scale” 
of Mr. Palmer, and with pleasure express my high admi- 
ration of it. It is constructed on the only principle. ac- 
knowledged by scientific men, since the invention of loga- 
rithms, adequate to such purposes. Over all sliding 
logarithmic scales it possesses a vast superiority, both in 
facility of use, and accuracy of result. For this superior- 
ity it is indebted to its circular form. With a diameter of 
about eight inches, it is equivalent to a common sliding 
scale of four feet, with its slide of the same length, making, 
when drawn out, a rod of about eight feet in length. It 
will be seen that its accuracy will be proportionably great- 
er, aS a circle can be constructed more exact than such a 
scale. G. C. WHITLOCK, 

Professir of Mathematics and Natural Science 
in Genesee Wesleyan Seminary. 


/ 


Mr. Aaron PaLtMEr—- 

Sir: I have taken much pleasure in testing the power of 
your “ Self-Computing Scale,” by examples from nearly all 
the arithmetical rules. I am particularly struck with its 
great facility and accuracy in computing interest, appor- 
tioni Re dividends, and performing proportions generally. 
From the best examination I have been able. to give it, I 
think it at once a most simple and wonderful invention ; 
and I am confident, that when perfected, it will come rap- 
idly into extensive public use, and will prove of singular 
benefit to those having occasion to make frequent compu- 
tations in bankruptcy, insolvency, insurance, averages, 
taxation, and the like branches of business. 

AMOS B. MERRILL, 
10 Court-street, Boston. 


PREFACE. 


At the suggestion of several intelligent friends 
who have become acquainted with my ‘ Compu- 
ting Scale,” I have been induced to present this 
simple volume to the public. The general princz- 
ple on which my Scales are constructed, is now 
acknowledged by all scientific men, as the only 
one adequate to perform computations mechani- 
cally. The rapidity, certainty, and accuracy of 
their results are now established beyond the pos- 
sibility of a doubt. The present volume can be 
afforded at a price which will place it within the 
reach of all. Those who wish to carry out their 
computations to a greater number of decimals, 
can have their wishes gratified in the purchase of 
“ Palmer’s Computing Scale,” which is nearly one 
foot square. All the errors which have peer ae 
covered in the former editions, have been corre 
in this ; and the present work may be regarded as 
nearly perfect. I only ask a candid examination 
of the work, and hope it may be as useful to the 
public, as I have, by long and arduous labor, 
‘sought to make it. ©, 

AARON PALMER. 

Boston, Feb. 15, 1844. 


DESCRIPTION OF THE SCALE. 


Tue lines on both parts of the Scale are precisely alike. 
That part of the Scale which revolves is called “the cir- 
cular,” and the other is called the “fized part.” The 
lines represent the exact position of the different figures, 
and are generally numbered. ‘The longest lines are num- 
bered 1, 2, 3, &c., and represent 1, 2, 3, oa .. or 10, 20, 30, 
&c., or 100, 200, 300, &c., or nr. a Pp» SCs according 
to the nature of the problem to be solved. The next sized 
lines represent 11, 12, 13, 21, 54, &c., or 110, 120, &c., 
and are nearly all numbered. The shortest lines represent 
the amount. or quantity, when it is composed of three 
figures, as, 101, 102, 125, &c., or 10-1, 12:5, &c., or 1:01, 
1:25, &c.; but on the Pocket Scale these lines are not 
numbered. ee 

To find 105 on the Pocket Scale.—Call the large I, 
100 ; 0; then count five of the short lines toward 11, and you 

we the point for 105. 

To find 224.—First find 22, (the two first figures in the 
teat) then count the short lines between 22 and 23; 
the first short line represents 223; the next short uae 
is 224. 

x find 645.—First find 64, (the two first figures in the 

unt,) then the only short line between 64 and 65 rep- 
resents 645. 


A TABLE OF 


UGE-POINTS USED ON 
IS SCALE. 


I., at the diamond, is the gauge-point for Multi- 
plication, Division, &c., &c. 

A. Area of a Circle. 

C. Circumference of a Circle. 

B. G. Beer Gallons. 

W.G. Wine Gallons. 

15. For months, at 8 per cent. 

1714. For months, at 7 per cent. 

2. For months, at 6 per cent. 


456 


521. 
608. 
107. 
_ 106. 
160. 
144. 


. For days, at 8 per cent. 


For days, at 7 per cent. 

For days, at 6 per cent. 

Compound Interest for years, at 7 per cent. 
Do. do. do. 6: don: 

For Acres. i he 

For Square Timber. : 


9. Yards Square. 


886. 
707. 
O77. 


Square and Circle, equal in Area. 
Inscribed Square. #. 
Side of Inscribedube. . 


87. Side of Inscribed Triangle. 


589. 


Side of Pentagon, (5 sides.) 


5. Side of Hexagon, (6 sides.) 
437. Side of Heptagon, (7 sides.) 


& 


10 


383. Side of Octagon, (8 sides.) 

337. Side of Nonagon, (9 sides.) 

31. Side of Decagon, (10 sides.) 
282. Side of Undecagon, (11 sides.) 
26. Side of Dodecagon, (12 sides.) 
464. Diameter of 3 Inscribed Circles. 
416. Diameter of 4 Inscribed Circles. 
785 . Point for Area. 

314 . Point for Circumference. 


il 


TO eee MULTIPLICATION. 


Ru.e.—First find the multiplier on the circular. 
Place it opposite 1; then opposite the multiplicand 
found on the fixed part is the product on the cir- 
cular. 

Example.—What i is the product of 4 by 2? 

Place 2 opposite 1; then opposite 4 is the pro- 
duct = 8. 

N. B.—Observe, now, that all the numbers and 
parts of numbers on the fixed part, are multiplied 
by 2, and their products are directly opposite them 
on the circular. So of any other multiplier. 


What is the product of 12 by 72 
Place 7 opposite 1; then opposite 12 is 84, the 
answer. 


Of 3 by 3? My, 
Place 3 opposite 1; then opposite 3 is 9, the 
answer. . 


What is the product of 8 by 23? r 
Place 2°5 Spprete 1; then opposite 8 is 20, the 
answer. 


What is the product of 10 by 5? 
bees 5 puppets 1; then opposite 10 is 50, the 


12 


answer. Here you have to use the same figures 
both times, calling them 1 and 5 the first time, and 
adding a cipher to each the next time. 


What is the product of 13 by 3? 
Place 3 opposite 1; then opposite 13 (found be- 
tween the large 1 and 2) is 39, the answer. 


What is the product of 50 by 4? 

Place 4 opposite 1: now we must call the large 
5, 50: opposite it is 200, the answer. 

What is the product of 24 by 3? 

Place 3 opposite 1; then opposite 24 (found be- 
tween the large 2 and the large 3) is 72, the answer. 


What is the product of 3 multiplied by -2, (two 
tenths ?) 

Now we must call the large 2. two tenths. Place 
it opposite 1; then opposite 3 is °6, (six tenths,) 
the answer. 


DIVISION. 


Ruie.—Find the divisor on the circular. Place 
it opposite 1; then opposite the dividend, found 
also on the circular, is the quotient on the fixed part. 

‘Example.—2 is in 8, how many times? 

Place 2 opposite 1; then opposite 8 is 4, the 
answer. ag ag 


13 


3 is in 12, how fnany times ? 
Place 3 opposite 1; then opposite 12 is 4, the 
answer. ¥ 


How many times 4 in 14 ? 
Place 4 opposite 1; then opposite 14 is 3 and 
five tenths, (3°5,) the answer. 


Norr.—Whenever a divisor is placed opposite 1, all the 
numbers and parts of numbers on the circular are divided 
by it. The quotients are on the fixed part. 

Example.—Place the divisor 2 opposite 1; now opposite 
2 is 1, opposite 12 is 6, opposite 4 is 2, opposite 6 is 3, op- 
posite 14 is 7, opposite 24 is 12, opposite 125 is 62:5, oppo- 
site 75 is 37:5, &c. 


To MuttrieLy BY ONE NUMBER, AND DIVIDE BY 
ANOTHER, BY ONE SIMPLE PROCESS. 


Rute.—Place the multiplier on the circular op- 
posite the divisor; then opposite the multiplicand 
is the result. a 

Example.—What is the result of 22 multip ied 
by 13, and divided by 14? 

Place 13 opposite 14; then opposite 22 is 204-1, 
the answer. 


FRACTIONS. 


To cHANGE AN ImpRoPER FRACTION TO A WHOLE 
or Mrxep Numser. 


Ruize.—Place the numerator found on the cir- 
g.. : 


14 


cular opposite the denominator ; then opposite 1 is 
the answer. — 

Example.—A man spending 7 of a dollar per 
day, in 8 days would spend 2 of a dollar. How 
much would that be ? 

Place 8 opposite 6; then opposite 1 is $1.33, 
the answer. 


In 2 of a dollar how many dollars ? 
Place 8 opposite 4; then opposite 1 is $2, the 
answer. 


To repuce 4 Mrxep NumpBer To AN IMPROPER 
FRACTION. 

Ruite.—Place the mixed number opposite 1; 
then opposite the denomination to which you wish 
it reduced, is the answer. 

Example.—tIn 16,°, of a dollar, how many 12ths 
of a dollar? lat 
Place 16,8, opposite 1; then opposite 12 is the 
er Of 12ths in 16,4, viz., 197 = 47, the 
answer. | 


To REDUCE A Fraction To 1rs LowEstT AND ALL 

irs ‘TERMs. 

Ru.te.—Place the numerator found on the cir-— 
cular, opposite the denominator ; then all the num- 
bers standing directly opposite each other, are 
other terms of said fraction; and the lowest of — 
said numbers are its lowest terms. 


15 


Reduce 34 to its lowest terms. 

Place 12 opposite 16; now 9 is opposite 12, 
(+,) 6 is opposite 8, (g,) and 3 is opposite 4, (2,) 
the answer. 


t 


To DIVIDE A FRacTION BY A WHOLE NuMBER. 


Rute.—Place the whole number, found on the 


circular, opposite 1; then, opposite the denominator 


is a number, which, placed opposite the numera- 
tor, is the answer. 

Example.—lf 2 yards of cloth cost 2 of a dollar, 
how much is that per yard ? 3 ; 

2 is in 2 how many times? Place 2 opposite 1; 
then ee 3.is 6. Now place this opposite 2, 
and it will read 2, the answer, = 1. . 

2 is in 7 how many times ? | 

Place 2 opposite 1; apie 8 is 16. This, 
placed opposite 7, rekon 75, the answer. 


To muttipLy A WHoLe Numper By A Fraction, 


orn A FracTION By A WHoLE NUMBER. 


Rute.—Place the numerator found on the cir- 
cular, opposite the denominator; then opposite the 
whole number is the answer. 

N. B.—Whenever a numerator is placed oppo- 


site a denominator, all the numbers on the circular 


are that fractional part of the numbers ys 
them. kot ae 


16 


Example.—Place 3 opposite 4; this is 3. Now 
the 3 is 2 of 4; 6 stands Boost 8, peiags of 8 ; 
9 is dppoalees 12; 3; 12 is opposite 16; &e., &c. Now 
move the circular until 3 is opposite 5; now all the 
numbers on the circular are 3 of those opposite 
them. 


_ Note.—Whenever a numerator is placed opposite a de- 
nominator, thereby forming a vulgar fraction, the decimal 
of said vulgar fraction is opposite 1; hence, 


To REDUCE VuLear Fractions to DecimaL 
f FRACTIONS. 

Route.—Place the numerator found on the cir- 
cular, opposite the denominator ; then opposite 1 is 
the decimal fraction. 

Example.—W hat is the decimal of 3? 

Place 3 opposite 4; now opposite 1 is *75, the 
i 


i is the decimal of 7? 
Place 7 opposite 8 ; Bopodite 1 is ‘875. 


To repuce Decimat FRAcTIONS TO VULGAR 
FRACTIONS. 


Ruie.—Place the decimal, found on the circu- 
lar, opposite 1; then any two figures standing 
directly opposite each other, is the answer. 

Example.—W hat = the vulgar fraction’ equiva- 
lent to the decimal -5 


17 


Place 5 opposite 1; now 1 is opposite 2 = 1, the 
answer. 


To MULTIPLY ONE FRACTION BY ANOTHER. 


Rute.—Reduce one to decimals; then place 
the numerator of the other opposite the denomi- 
nator: then opposite the decimal is the answer in 
decimals, which, if desired, can be reduced to a 
vulgar fraction by the preceding rules. . 


To REDUCE THE DIFFERENT CURRENCIES TO FEDERAL 
Money. 


Ruie.—Place the 1 on the circular, opposite the a 


number of shillings and parts of a shilling compo- 
sing a dollar of the currency to be reduced; then 
opposite the given-number of shillings is the answer. 
Example.—Reduce 5 shillings, New York cur- 
rency, to Federal money. 
Place 1 (on the circular) opposite 8; then oppo- 
site 5 shillings is 625, the answer. aa 


In 15 shillings, how much ? 
Opposite 15 is 1-875, the answer. 


In 32 shillings, English currency, how much ? 
Place 1 (on the circular) opposite 4:5; then op- 
- posite 32 is $7°11, the answer. 


In 9 shillings, how much ? 
Opposite 9 is $2, the answer. 
Q* 


18 


INTEREST. 


To compute INTEREST FOR YEARS. 


Ruize.—Place the rate per cent. found on the 
circular, opposite 1; then opposite the principal is 
the interest. | 
Example.—What is.the interest of $50, at '7 per 
cent. ? | 

Place 7 opposite 1; then opposite 50 is $3-°50, 
the answer. 


What is the interest on $40, at 64 per cent. ? 


Place 6:5 opposite 1; then opposite 40 is $2°60, 
the answer. | 


To compute Interest For Monrus. 


Rurzr.—Place the principal (found on the circu- 
lar) opposite the gauge-point for months, at the 
given per cent.; then opposite the given number 
of months is the answer. | 

Example.—W hat is the interest on $50 for three 
months, at 7 per cent. ? 

Place 50 (found on the circular) opposite 1714 ; 
(the gauge-point for months, at 7 per cent.;) then 
opposite 3 months is ‘875, the answer. 


\ 


What is the interest on $60 for eight months, at 
6 per cent. ? 


19 


Place 60 opposite °2, (the gauge-point for 
months, at 6 per cent.;) then opposite 8 months is 
$2°40, the answer. 


To compute INTEREST FoR Days. 


Ruie.—Place the principal (found on the circu- 
lar) opposite the gauge-point for days at the given 
per cent.; then opposite the number of days is the 
answer. | 

Example.—W hat is the interest on $55 for 15 
days, at 6 per cent. ? 

Place 55 opposite ‘608, (the gauge-point for 
days, at 6 per cent.;) then opposite 15 days is 
°135, (thirteen cents and five mills,) the answer. 


_ Tue PRINCIPAL AND INTEREST BEING GIVEN, TO 
FIND THE RATE PER CENT. 


RULE For ONE YEAR.—Place the interest opposite 
the principal ; then opposite 1 is the rate per cent. 

Example.—Received $7:00 for the use of $50-00 
for one year: what was the rate per cent. ? » 

Place 7 opposite 50; then opposite 1 is 14, the 
answer, (14 per cent. ) 


Gave $4:00 for the use of $80°00 one year: 
what was the rate per cent. ? 

Place 4 opposite 80; then opposite 1 is 5, the 
answer, (5 per cent.) 


20 


Rute ror Montus.—Place the given interest op- 
posite the given number of months; then observe 
the number opposite 12. Now place this number 
opposite the principal ; then opposite 1 is the rate 
per cent. 

Example.—Paid 25 cents for the use of $5:00 
for 4 months: what was the rate per cent. ? 
“Place 25 opposite 4; then opposite 12 is 75. 
Now place 75 opposite $5:00; then opposite 1 is 
15, (15 per cent.,) the answer. 


Gave 14 cents for the use of $60-00 one month : 
what was the rate per cent. ? 

Place 14 opposite 1; then opposite 12 is 1-68. 
Now place 1:68 opposite 60; then opposite 1 is 
2°8, (2,8, per cent.,) the answer. 


Rue ror Days.—Place the given interest oppo- 
site the given number of days; then observe the 
interest opposite 365, (the number of days in a 
year.) Place this opposite the principal ; then op- 
posite 1 is the rate per cent. 

Example.—Paid 14 cents for the use of $64: 00 
for 29 days: what was the rate per cent. ? 

Place 14 opposite 29: now opposite 365 is 
$1-76. Now place 1:76 opposite 64; then oppo- 
site 1 is 2°75, (23 per cent.,) the answer. 


Paid 28 cents for the use of $50-00, for 21 
days: what was the rate per cent. ? | 


21 


Place 23 opposite 21: now opposite 865 is 4. 
Place 4 opposite 50; then opposite 1 is 8 per cent., 
the answer. 


‘THE Rate PER CENT. AND THE INTEREST BEING — 
GIVEN, TO FIND THE PRINCIPAL. 

RuLe ror one YEAR.—Place the rate per cent. 
opposite 1 ; then opposite the interest is the principal. 

Example.—At 7 per cent. I paid $3-50 for the 
use of money 1 year: what was the principal ? 

Place 7 opposite 1; then opposite 3:50 is $50-00, 
the answer. 


Rute ror Montus.—Place the interest opposite 
the given number of months; then opposite the 
point of the given per cent. for months, is the 
answer. 
_ Example.—Gave $2:00 at 7 per cent. for three 
months: what was the principal ? 

Place 2 opposite 3; then opposite 1:714 is 
$114-30, the answer. 


Rute ror Days.—Place the given interest op- 
posite the given number of days; then opposite 
the gauge-point for days stands the principal. 

Ezample.—At 7 per cent., gave 15 cents for 20 
_ days: what was the principal ? 

Place 15 opposite 20; then opposite 521 (thie 
gauge-point for days, at 7 per cent.) is $39-00, the 
answer. 


22 


Tue RATE PER CENT., INTEREST, AND PRINCIPAL 
BEING GIVEN, TO FIND THE TIME. 


Rute.—Place the interest of the given principal 
for one year, opposite 12; then opposite the given 
‘interest will be the answer, in months and deci- — 
mals of a month. Or, place the interest of the 
given principal for one year opposite 365; then 
opposite the given interest will be the time in 
days. it: 

Example.—Gave 87:5 cents, at 7 per cent., for 
$50:00: how long did I have it ? 

The interest of $50-00 for one year is $3°50. 
Place 3°50 opposite 12; then opposite ‘875 is the 
answer, 3 months. 


Gave 24 cents, at 7 per cent., for the use of 
$50:00: how long did I have it ? 

Place $3-50 opposite 365; then opposite 24 is 
the answer, 25 days. 


Compounp INTEREST. 


Rute.—Place the principal opposite fig. 1; then 
opposite the rate per cent. added to 100, on the 
fixed part, is the amount for one year. Place this 
amount opposite fig. 1; then opposite the same 
point is the amount for two years. Place this last 
amount opposite 1; then opposite the same point 
is the amount for three years, &c. 


23 


Example.—What is the compound interest on 
$5:00 for 5 years, at 6 per cent. ? 

Place 5 opposite 1; then opposite 106 (the per 
cent. added to 100) is $5:30, the amount for 1 year. 
Now place $5-30 opposite 1; then opposite 106 is — 
$5-62, the amount for 2 years. Now place $5:62. 
opposite fig. 1; then opposite 106 is $5°95, the 
amount for 3 years. Now place $5:95 opposite fig. 
1; then opposite 106 is $6-31, the amount for 4 
years. Now place $6°31 opposite fig. 1; then 
opposite 106 is $6°69, the amount for 5 years. 


LOSS AND GAIN. 


Bought a hogshead of molasses for $60: for 
how much must I sell it to gain 20 per cent. ? 
-Rute.—Place 20 opposite 1; then opposite 60 
is what must be added to the original cost to gain 
said per cent., viz. 12; which added to 60=72. 


Bought cloth at $2°50 per yard; but, being 
damaged, [ am willing to sell it so as to lose 12 
per cent. How must I sell it per yard ? 

Place 12 opposite 1; then opposite $2°50 is °30, 
the amount to be deducted from $2-50, which will 
leave 2°20, the answer. 


Bought cloth at 50 cents per yard; sold it for 
10 cents advance from cost. What per cent. did 
I make ? 


24 


Place 10 opposite 50; then opposite 1 fs 20 per 
cent., the answer. 


AnotHer Metuop.—Place the original cost op- 
posite 1; then opposite the rate per cent. added to 
100, is the answer. 

Example.—Bought corn at 50 cents per bushel : 

at how much must I sell it to gain 20 per cent. ? 

Place 50 opposite 1; then opposite 120 is 60 

cents, the answer. 


Bought cloth at $2 per yard, and sold it at $3 
per yard: what per cent. did I make ? 

Place 2 opposite 1; then opposite 3 is 150, 50 
per cent., answer. 


RULE OF THREE, OR PROPORTION. 


-Rue.—Place the second term opposite the first ; 
then opposite the third term is the answer. 
Example.—lf 2 yards of cloth cost $4:00, what 
cost 8 yards ? 
Place 4 opposite 2; then opposite 8 is 16. 


Nore.—All numbers of yards, at that rate, are now on 
the scale, and may be determined without moving the 
circular. 


At 7 of a dollar per yard, what cost 4 yards ¢ 2 
Place 7 opposite 8; then opposite the given 
number of vards. is the answes Ny 


we 


a ibe 
est 


20 


oe 


If 1 ton of hay cost $8:00, what cost 900 
pounds ? . 

Place 8 opposite 2000, (the number of. Ibs. ina 
ton;) then opposite 900 is the answer : and so off 
any other number of pounds. . 


FELLOWSHIP. 


Rute. Place the whole gain or fs opposite 
the whole stock ; then opposite each man’s share 
of the stock, is bis share of the gain or Joss. 
Example.—A invested $30, B invested $20, 
and they gained in trade $12: what is each goon 
share of the gain? 
Place 12 (the whole gain) opposite 50, (the 
whole stock ;) then opposite 20 (A’s stock) is 
$4°80, and opposite 30 (B’s stock) is $7:20. 


EVOLUTION. 


To EXTRACT THE SquaRE Root. 
RuLE.—Move the given number around until it 
is opposite the same “number which is opposite 1; 
and that number is the answer sought. ~ 
- Example.—What is the square root of 42? 
Move 42 on the circular around until it comes 
opposite 6°48. Now 6:48 is opposite 1; hence 
that is the square root of 42. 


| pi To extract THE Cuse Root. 


_Rute.—Move the given number around until it 
| , ane 


26 


comes opposite a number, the square of which at 
é the same time is opposite 1; and that number is 
the root sought. 

‘zample.—W hat is the cube root of 27? 
- love 27 around until it comes opposite 3; at 
‘that time 9 is ORR Og Be as 3 is the answer. 


“TO APPORTION TAXES. 


Rute.—Place the whole tax to be raised, found 
on the circular, opposite the whole valuation ; then 
opposite each man’s valuation, is his tax. 

Example.—A tax of $1.500°00 is levied on a 
valuation of $200.000-00 : what is a man’s tax 
whose valuation is $700-00 ? 

Place 1500 opposite 200.000; then opposite 
700 is $5-25, the answer. 


Scuoou Tax. 


1550 days have been sent, and $33:20 tax is to 
be raised: how much is each man’s tax ? 

Place 33°20 opposite 1550; then opposite the 
days each man has sent, is his tax. | 


A has sent 28 days ; his tax is 60 cents. 


Opposite 70, the number of days B has sent, is_ 
his tax, $1-50; and so of every other man’s t x, 
without moving the scale. ~ ; ¥ 


Dial 


ee 


27 
TO COMPUTE TOLL. 


at 4 mills per mile per 1000 poun 

Place the 4 opposite 1000 ; opposite 6 is :02 
(two cents four mills.) Now ace this opposite 1 ; 
then opposite 289 is $6°936, the answer. , 


What is the toll on 6000 pound + 289, “> 


TO MEASURE SUPERFICES. 


oe 1.—Place the width in inches opposite 
; then opposite the feet in length is the caeuiel 
in a and tenths of a foot. 
Example.—Give the contents of a board 6, inch- 
es wide, 14 feet long. 
Place 6 opposite 12; then opposite 14 ane 
pence is the answer, 7 fest. 


Rue 2.—Place the width in nteet opposite 1; then 
opposite the length in feet, is the answer in ee 


How many square feet in a floor 20 by 20 ? 
20 X 20=400, the answer. 


ae How many square feet.in a garden 
q 96 by 54 feet ? ' 
Ne 96 X54=5184 feet, the answer. 


am -Nore.—If one side be. inches, and the other feet, place 
i the givens number of inches opposite the number of inches 
eM 


i 


pr a lot oe 
many acres ? 


in a foot, viz. 12; then opposite the length in feet will be 
the answer in feet. If one side be feet, and the other rods, 
the answer will be in rods, by placing the feet opposite the 
number of feet in a rod, &c., &c. 


d 120 rods long and 60 rods wide, 


Place 60 opposite 160, (the number of rods in an 
acre;) then opposite 120 is 45 acres, the answer. 


If a board be 8 inches wide, how much in 
length will make a square foot ? 

Place the width, 8 inches, opposite 1; then op- 
posite 144 (the number of square inches in a 
foot) is the answer, 18 inches. 


If a piece of land be 5.rods wide, how many 
rods in length will make an acre ? 

Place 5 opposite 1; then opposite 160 (the 
number of rods in an aera). is the answer, 32 rods. 


SQUARE YARDS. 


How many square yards of carpeting will it re- 
quire to cover a floor 20 feet long and 14 feet wide ? 

Place 20, found on the circular, opposite 9, (the 
gauge-point for yards square;) then opposite 14, 
on the fixed part, is 31 yards, the answer. 


Tue WipTH AND CONTENTS GIVEN, TO FIND THE 
LENGTH. 


Ruie.—Place the contents on the circular, op. 


29 


posite the width in feet; then opposite 9, on the 
fixed part, is the length in feet, 
, Example. —TI have a room containing 20 square 
yards ; I wish to cover it with a piec e Df carpeting, , 
2 feet wide: how many feet in length will it resy 
quire ? eats, rr 
Place 20 on the circular opposite 2°5, (215) then =~ 
opposite 9, on the fixed part, is 72 feet, the answer. 


To MEASURE LAND IN CHAINS AND LINKS. 


Ruxte.—Place one of the sides,-in chains and 
links, opposite 1; then opposite the other side, in 
chains and {inica; is the number of acres and parts 
of an acre. 

Example.—To find the acres in 7 chains aod 50 
links by 6 chains and 40 links. 

Fa ie 750 opposite 1; then opposite 640 is 4:80 

4 89.) acres, the answer. 


To find the acres in 7 chains and 75 links by 9 
chains and 64 links. - . 

Place 775 opposite 1; then opposite 964 is 
Tgp acres, the answer. 
To find the amount of land in 1 chain and 80 
_ links by 2 chains and 50 links. 
Place 180 opposite 1; then, opposite 250 is 45 


(475) of an acre, the answer. 
3* 


30 


To MEASURE SQUARE TIMBER. 


Rute.—Place the product of the width by the 

thickness, opposite 144; then opposite the length 
: ate answer in feet hid tenths. : 

Example.—W hat is the solid contents of a stick 
4 inches by 7, and 20 feet long ? 

4xX7=28. Place 28 opposite 144; then oppo- 
site the length, 20 feet, is 3°9 feet, the an- 
swer,=3,, feet. 


‘ What is the solid contents of a stick of timber 
18 inches by 18 inches, and 138 feet long ? 

The product of 18 by 18, is 324. Now place 
324 opposite 144; then opposite 13 (the length) is 
29°3, (29,3,,) the answer. 


N. B.—If it be desired to have the answer in 
inches, instead of placing the product of the width 
by the thickness, opposite 144, place it opposite 1; 
then opposite the length in inches, will be the 
solid contents in inches. . 


Notr.—Any bale, box, or chest may be measured by the 
preceding rule. 


To MEASURE A HyPpoTENUvsE. 


B ' 
aie aB hypotenuse, nc perpendicular, ac base. 
A C 


RuLe.—Square each of the sides, and add their 


31 


products together, the square root of which is the 


answer. , x” 
Example.—What is the hypotenuse of a right 


angled triangle, one side of which is 3 feet, the . 
other 4 feet ? ma 

3X3=9, and 4x4=16; these two added ion 
gether make 25, the Sine root of which is § 
feet; the answer. 


/\ To MEASURE A TRIANGLE. 

Place half the base opposite 1; then op- 
posite the perpendicular height, is the area. 

Example.—W hat is the area of a triangle whose 
base is 32 inches, and perpendicular height 14 
inches ? 

Place 16 (1 of 32) opposite 1; then opposite 14 
is 224 square inches, the answer. 


> 
ae 


To FIND THE SoLip CoNnTENTS OF A PYRAMID. 


Ru.te.,—Multiply the area of the base by 
1 of the perpendicular height, whether it be 
a square, triangular, or circular pyramid. 

Example.—W hat isthe solid contents of a pyr- 
- amid whose base is 4 feet square, and perpendicu- 
lar height 9 feet ? : 

4X4=16, the base. Place this opposite 1. 
Now i of 9 is 8, Opposite 3 is the solid contents, 
48 feet. 


32 


‘There is a cone whose height is 27 feet, 
and whose base is 7 feet in diameter: what 
are its contents ? 

_ Place the square of 7 (49) opposite 1; then op- 
posite a is the area of the base. 

1 of 27 is 9. Place 9 opposite 1; then opposite 
the area (38-6) is the answer, 3461 solid feet. 


To FIND THE Sotip ConTENTS oF A FrustuM oF 
A. PYRAMID. 

~Rutze.—To the product of one end by the other, 
add the sum of the squares of each end. Place 
this opposite 144. Then opposite + of the length, 
is the answer. : 
- Example.—What are the contents of a stick of 
timber whose larger end is 12, whose smaller end 
is 8 inches, and whose length is 30 feet ? 

The product of one end by the other is 96, the 
square of 12 is 144, the square of 8 is 64. These, 


all added, make 96 
144 
64 


304. Place this opposite 144 ; 
then opposite 10 (4 of the length) is the answer, 
21} feet. el 


33 tl 


To FIND THE SoLip ConTENTS OF A FRustuMm OF 
A Cong. 


Rute.—Multiply each diameter by itself sepa- 
rately ; multiply one diameter by the other; add 
these three products together. Now place the 
length opposite 382; then opposite the products 
thus added, is the answer. 


To find the Circumference of a Circle from its Di- 
ameter, or its Diameter from its Circumference. 


© Rute.—Place letter c (found on the circular) 
opposite fig. 1; then the figures on the fixed part 
are diameters, “and those on the circle are circum- 
ferences. Opposite each diameter is its circum. 
ference. 

Example.—What is the circumference of a 
circle whose diameter is 9 inches ? 

Place c opposite fig. 1; then opposite 9 is 28°2, 
(28 inches and 2 tenths,) the answer. 


To find the Area of a Circle. 


C:) Rute.—Place the square of the diameter 


opposite 1; then opposite the letter a is the 
area. 
Example.—W hat is the area of a circular gar- 
den whose diameter is 11 rods ? 
Place 121 (the square of 11) opposite 1; then 
opposite the letter a is 95-03 rods, the answer. 


w 34 


To find the side of a Square equal in area to any 
given Circle. 


Ruie.—Place *886, found on the cir- 
cular, opposite fig. 1; then opposite any 
diameter of a circle upon the fixed part, is the side 
of a square equal in area, on the circular, 
Example.—What is the side of a square equal 
in area to a circle 4 feet in diameter ? 
Place 886 opposite fig. 1; then opposite 4 is _ 


3°55 feet, the answer. # 


To find the side of the greatest Square that can be 
inscribed in any given Circle. 


Ruie.—Place ’707, found on the cir- 
cular, opposite fig. 1; then opposite any 
diameter of a circle, (found on the fixed part,) is 
the side of its inscribed square. 
Example.—What is the side of an inscribed 
square equal in area to a circle 45 rods in diameter? — 
Place ’707 opposite fig. 1; then opposite 45, on | 
the fixed part, is 31°8 rods, the answer. 


To find the length of .one side of the greatest Cube 
that can be taken from a Globe of a given diam- 
eter. 

Ruie.—Place 577, found on the circular, oppo- 
site fig. 1; then opposite any diameter, on the fixed 
part, is the length of one side of the greatest cube. © 


3D 


Example.—W hat is the length of the side of the 
greatest cube that can be taken from a globe 82 
inches in diameter ? 

Place 577 (the eae for the side of an 
inscribed cube) .opposite fig. 1; then opposite 82, 
on the fixed it is 47°3 (479 x) ines the answer. 


To find. the Men of the side of the greatest equi- 


lateral triangle that can be inscribed in a 
Cyr circle. : 
4 Ru.te.—Place 87, found on the circu- 


lar, opposite fig. 1; then opposite any diameter on 

the fixed part, is the length of the side of an in- - 
scribed triangle. And opposite the length ot the 
side of any frianale, on the aizenlan | is the diame- 
ter required to inscribe it in. * 

Example.—W hat is the length of one side of the 
greatest equilateral triangle that can be inscribed 
in a circle 62 inches in diameter ? 

Place 87 opposite fig. 1; then opposite 62, on 
the fixed part, is 54 inches, the answer. 


What is the least diameter of a circle in which 
a triangle may be inscribed, whose side is 6-5 
inches, (64) ? 

Place 87 opposite fig. 1; then opposite 6°5, on 
‘the prone is vA 48 (7-485) sad, the answer. 


36 

To find the length of the side of the greatest figure — 

that can be inscribed in a given Circle. ; 
Rue.—For a 

Pentagon (5sides) Place 589. 
Hexagon Gait Fee 
Heptagon 7 “ “487. 
Octagon 8 “ «) 3-83 
Nonagon aaa “337 
Decagon: (| 20: Fo A 
Undecagon 11 “ Fo ae x 
Dodecagon 12 “ aie 


opposite fig. 1; then opposite any given diameter 


on the fixed part, is the length of the side of the 
greatest figure that can be inscribed in it. 
Example 1.—What is the length of one side of 


4 


i 


the greatest pentagon, or five-sided figure, that can — 


be inscribed in a circle whose diameter is 51 inches ? 
Place 589 opposite 1; then opposite 51, on the 
fixed part, is 30 inches, the answer. 


Example 2.—What is the length of one side of 
the greatest nonagon (nine-sided figure) that can 
be inscribed in a circle 82 feet in diameter ? 

Place 337 opposite fig. 1; then opposite 82, found 
on the fixed part, is 27-6 (27,8,) feet, the answer. 


Example 3.—W hat is the least diameter of a cir- 
cle in which may be inscribed an undecagon, 


37 


(eleven-sided figure,) one side of which is 18 
inches long ? 
Place 282 opposite fig. 1; then opposite 13 inches, 


found on the circular, is 46° 1 inches, the answer. 


To find the greatest diameter of each of three equal 
eN Circles that can be inscribed within a Lir- 

26 cle of a given diameter. 

OF Rute.—Place 464 opposite fig. 1; then 

opposite any diameter on the fixed part is the Aes 


eter of one of the three inscribed circles. 


Example.—W hat is the greatest diameter of each 
of three circles, that can be inscribed within a cir- 
cle 25 inches in diameter ? 

Place 464 opposite fig. 1; then opposite 25 on 
the fixed part, is 11:6 aeleh. the answer. 


To find the greatest diameter of four equal Circles — 
that can be inscribed within another Circle 
of a given diameter. 


Rute.—Place 416 opposite fig. 1; then 
opposite any given diameter on the fixed part, is 
the diameter of each of the four inscribed circles. 

Example.—What-is the greatest diameter of 
each of four equal’ circles; that can be inseribed i DY, 
another circle#22 inches in diameter ? 

Place 416 opposite fig. 1; then opposite 22, on 
the fixed part, is 9:15 (9, Sy i) inches, the answer. 

4 


38 


To find the solidity of a Cylinder, or to measure 
* Round Timber. 


Rute.—First find the area of the 

===> base by the rule for finding the area 
of a circle; place that area opposite 144; then 
opposite the length in feet is the answer, in feet 
and decimals of a foot. 


Note.—If the diameter be given in feet, place the area 
opposite 1, instead of placing it opposite 144. 


Example.—W hat are the solid contents of a cyl- 
inder 5 inches in diameter, and 13 feet long ? 

Place 25 (the square of 5) opposite 1; then op- 
posite a is 1:965. Now place 1-965 opposite 144; 
then opposite 13 (the length) is 1°77 feet, the an- 
swer. 


How many solid feet in a round log 15 inches 
in diameter, and 14 feet long ? 

Place 225 (the square of 15) opposite 1; then 
opposite a is 1°77, the area. Now place 1°77 oppo- 
site 144; then opposite 14 is 17:2 feet, the answer. 


In a log 12 feet long, 14 inches diameter ? 
Answer, 12:8 feet. 


%., 
% 


In a log 16 feet long, 11 inches in diameter ? 
Answer, 10-5 feet. 


39 


In a log 7 inches diameter, 15 feet long ? 
Me Ries 52. feet. 


Notr.—li the diameter and length are both given in 
inches, place the square of the diameter opposite 1728; 
then opposite the inches in length is the answer in feet. 


Nots.—A cylinder that is 12 inches in diameter and 12 
inches long, and a globe that is 12 inches in diameter, and 
a cone that is 12 inches high and 12 inches diameter at its 
base, bear a proportion to each other as 3,2,and1. 'There- 
fore, if you place the contents of any cylinder on the circu- 
lar opposite to 3 on the fixed part, then opposite 2 on the 
fixed part is the contents of an inscribed globe, and opposite 
fig. 1 is the contents of an inscribed cone. 


To find how many solid feet a round stick of Timber 
will contain, when hewn square. 


Ruie.—Place double the square of half the 
diameter opposite 144; then opposite the length is 
the answer. , 

Example.—In a log 28 feet long, 22 inches di. 
ameter, half the diameter is 11, the square of 
which is121. ‘This doubled, is 242. Now place 
242 opposite 144; then opposite 28 (the length) is 
47 + the answer. 


To find how many feet of Boards can be sawn from 
a Log of given diameter. ; 


Ruize.—Find the solid contents of the log when 


5 | 


40 


made square ; then place 12 opposite the thickness 
of the board, (including the saw-calf;) then oppo- 
site the solid contents is the answer in feet. 


To find the Area of a Globe or Baill. 


@ Rute.—Place the diameter opposite 1; 
—= then opposite the circumference is » the 
answer. 
Example.—How many square inches of leather 
will cover a bail 33 inches in diameter ? 
Place 33 opposite 1; then opposite p. is 11, the 
circumference. Opposite 11 is the area, 383 inches. 


How many square feet on the surface of a globe 
4 feet in diameter ?. 

Place 4 opposite 1; then opposite p. is 12°55 
feet, the circumference. Opposite 12°55 is 50:4, 
the answer. 


To find the solid contents of a Globe or Ball. 


Ruie.—First find its area by the prece 
ding rules; then multiply its area by } of 
its diameter. 

Example.—W hat are the solid contents of a ball 
14 inches in diameter ? 

Place 14 opposite 1; then opposite p. is 44 inch- 
es, the circumference. Opposite 44 is 617, the 
area. 4} of the diameter is 2°331. Place this op- 


% 


45 


ba OZ. é 
‘Pure Platina,. . 23000\Clay, . . . . 2160 


/ Fine Gold, . 19400. 
/ Standard Gold, . 17720 
~ Quicksilver, . . 13600 
| aA, PRR peel Ss OS 210 
Mine Silvers)... 11091 
~ Common Silver, . 10535 
f) Copper, *.\@ .. 9000 
+» Copper Pence, . 8915 
) Gun Metal, . . 8784 
Cast Brass, . . 8000 


Bolsa teas hig 1800 


AOI Lh de ed, TOAD 
Gast ion,;. |. we-t425 
ee eS ae - 7320 
— Crystal Glass, . 3150 
fm Granite, .. ...... 3000 
_ White Lead,. . 3160 
Merve, ys va 6 2100 
Hard Stone, . . 2700 
Green Glass,. . 2600 
Blinds, fora gin QROeD 

Common Stone, . 2520 


Notr.—The several sorts 
dry. Also, as a cubic foot 


Specific Gravity and Weight of Bodies. 


Brick, I . 2000 
Gamnnon Earth, 1984 
Nitte; os cae E900 
Tvortygss kee 
Brimstone, . . 1810 
Solid Sen baie 1745 
Sandye 3X 1520 
Coder hie a Te 
Mahos AY, os D068 
Boxwood, «fs 1030 
Sea AWaten, 28. 3) PO30 
Common Water, . 1000 


Oaks. aig 925. 


Gunp’d’r chick binee 937 

“« ina loose nea 836 
ASH) tel 800 
Maple, ee ee One TERE 
Beech; 3.54 “FOO 
Hele, 2 Soe oe ee GOO 
Bree eet oe 0 | he oo 
Corky. te oa eee ue nae eO 
Air at a mean state, i 


of wood are supposed to be 
of water weighs just 1000 


ounces, the numbers in this table express, not only the 
specific gravities of the several bodies, but also the weight 
of a cubic foot of each, in avoirdupois ounces ; and there- 
fore the weight of any ‘other quantity, or the quantity of 


any other weight may be found, as in the next two Aran: } 


sitions, 


om 


“ah 
¥ 


To find the Magnitude of any Body from its , Weigl 


Rurz.—Place the weight of the material in 
» ounces under its specific: gravity ; then opposite 
1728 is its magnitude 1 in cubic inches ; and oppo. | 
site 1 is the answer in cubic feet. ‘4 
- Example.—How many cubic inches of sunpow- 
der are there in one pound weight, shaken close ? 
Place 16 (the number of ounces:in a pound) — 
posite 937; then gpproste 1728 is its Content or 
magnitude, 29} % Inc 


How many cubic inches are there in 3 pounds . 
of cast brass ? ’ : 
Place 48 (the number of ounces in 3 pounds) 
opposite 8000 ; then opposite 1728 is the answer, 

103°5. 


To find the Weight of a Body from its Magnitude. 


RuiE.—Place the contents of the body opposite 
1728; then opposite its specific gravity is its 
_ weight in ounces. 

How many ounces avoirdupois in 864 cubic 
inches of sand ? 

Place 864 opposite 1728; then opposite 1520 
(the specific gravity of sand) is 760 ounces, the 
answer. 


- 5,280 feet i in a mile. 

63,360 inches in a mile. 
90,080 barley-corns in a mile. 
32,000 ounces make onefon. 
3,060 quart feet in an. acre. : 
4, 840 square yards in an acre. 


32 gillyin one wine-gallon. _ 
ae —-* gill, 
cubit inches in a pint. 
57-75 cubic inches in a quart. ee 
23 150: Ad cubic inches in a bushel. gy 
1: 2444 cubic fect in a bushel. pe 
3,600 seconds in an hour. 
86,400 seconds in a day she 
57,600 seconds in a year. Lee 
1,728 cubic inches in a foot. iA 


enty-four hours, 


128 feet make one cord of wood. ay, a 
. : e gs . Bi i a 


# 


* and 2 barrels of water. 


Comparative Value and Weight of diffe 
of Fire-wood, assuming as a standar 

vA bark Hh ckory. re 
Lbs. ina Set Bovinas val. 


Shell-bark Hickory, 4469 100 
Button Wood, “2891 9 52 


Mapls,  .. oty. We Boe @ gay i 
Black Birch, 8118s we 68 eo 
_ White Bloke. 5h BBO 3: oe bis 
~- White Beech, te te Dog MOD 
White Ash, — a 3420 TESS aD 
- Common Walnut, OAL On Ogee ae 
Pitch Pine, — nig Se) 1904 43° po), wet 
White Pine, © SE ABE Be Sox AD a pe 
Lombardy Popa, so VISE OREO Se 
Apple Tree, | #3115 70am 

_ White Oak, 3821 0.6). BL Seen 
Black Oak, ee: eh OG mee 
Scrub Oak, 3337 18 : ek 
Spanish Oak, eae | eae 52 gd 

® Yellow Oak, °’ «veo 2919" > * Cage 

~ Red Oak, 3204.0" 5, C985 ae 
White Elen, , 2502 » UBB a 
Swamp inca 3361 73. 9 4 


‘ 


TUT 


. 
FTEs ce 


